WEBVTT
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uh, okay. Sketch the region closed by the
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given curves and finance area. So first, let's
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draw those two curves. This is our XY plane
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. And, uh, the first function is X
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equals. So why to the power floor? So
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it looks like a problem, but it grows much
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faster. So it opens to the right like this
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. This will be my ex seacoast y to the
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power four. Oh, and then the second term
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here, Um, why he goes to the square
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root of two minus x. Yeah, this we
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know. Oh, yeah. Um, it can
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be represented as if we take the square. This
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is just a wide square equals two to minus X
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. We move around things. This is equivalent with
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X equals two two. Wine is Y square.
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What? Let's score. Yeah, and, uh
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, be careful here. We also need this indication
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why is greater or equal to zero? Because you
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know, the square root my equal to the square
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root of something, So why cannot be negative?
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Yeah. Okay. And this is also a problem
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. He opened to the left on a start at
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two. And open to the left. Okay.
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They will be enclosed area will be here. Okay
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. And here is to Here is General Oh,
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uh, and as we can see, um,
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since we reformat the second curve right now, everything
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is represented by why. So if we want to
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find an area and take the integral with respect to
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why, instead of facts and and the boundaries at
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this point in this point, So if I do
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know this s by one Yes. S y two
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how to find them? It's just, um Oh
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, be careful here. The enclosed region is actually
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now the entire thing, because we could this extra
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condition here when we reformulate the second curve, why
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should be no negative. So, um, this
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enclosed area is only this half of them is here
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. Here is empty. Okay. Um, therefore
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, we don't have this by one. We only
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have this fight to on our right. One will
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be zero. It goes from zero to white too
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. Okay. Mm hmm. So now we know
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. Mm. Our boundary by one will be terrible
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. And why to surely satisfy in a way to
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is positive. So what? You should satisfy two
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minus. Why square the second curve and the first
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curve echoes too wide. The power of four.
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Okay. Mm. Uh, as we can see
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, if I plug in by coast to one.
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This equation hopes so you can say are way too
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. Must be one. Okay. Or you can
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do the factoring Then you can solve for this,
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uh, um, polynomial equation, you'll find your
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roots, and the positive route will be our right
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to, and it has to be one. Um
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, So the boundary will go from 0 to 1
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. Um, seeing inside the integral is the record
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minus left, Curve like curve. Here is just
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two minus. Why? Square minus the left.
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Her left her is, uh, right to the
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power of four. An anti duty of that is
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to why mine is one third like cube, minus
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month. Faith, my faith and inveterate one and
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zero and receiving Michael 20 this whole thing you go
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to zero. So we only care when y you
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go to one plug in white. Go to one
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. We got two minus one third, minus one
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faith. So it will be on two minus one
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third. My nurse on fifth. So this this
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is, uh, 8/15, right? So it
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will be 30/15 miners, eight or 15. Oh
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, So this whole thing will be, um,
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24. 22 over 15. Mm, 15.
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Okay.